Symplectic monodromy at radius zero and equimultiplicity of $\mu $-constant families

Abstract

We show that every family of isolated hypersurface singularities with constant Milnor number has constant multiplicity. To achieve this, we endow the A’Campo model of “radius zero” monodromy with a symplectic structure. This new approach allows us to generalize a spectral sequence of McLean converging to fixed point Floer homology of iterates of the monodromy to a more general setting that is well suited to study $\mu $-constant families.

Authors

Javier Fernández de Bobadilla

IKERBASQUE, Basque Foundation for Science, Bilbao, Basque Country, Spain and BCAM, Basque Center for Applied Mathematics, Mazarredo, Bilbao, Basque Country, Spain and Academic Colaborator at UPV/EHU

Tomasz Pełka

BCAM, Basque Center for Applied Mathematics, Mazarredo Bilbao, Basque, Country, Spain and Institute of Mathematics, University of Warsaw, Warsaw, Poland